356 research outputs found
Multiscale Gaussian Random Fields for Cosmological Simulations
This paper describes the generation of initial conditions for numerical
simulations in cosmology with multiple levels of resolution, or multiscale
simulations. We present the theory of adaptive mesh refinement of Gaussian
random fields followed by the implementation and testing of a computer code
package performing this refinement called GRAFIC2. This package is available to
the computational cosmology community at http://arcturus.mit.edu/grafic/ or by
email from the author.Comment: 38 pages. Submitted to ApJ Supplemen
Dependence of the Inner DM Profile on the Halo Mass
I compare the density profile of dark matter (DM) halos in cold dark matter
(CDM) N-body simulations with 1 Mpc, 32 Mpc, 256 Mpc and 1024 Mpc box sizes. In
dimensionless units the simulations differ only for the initial power spectrum
of density perturbations. I compare the profiles when the most massive halos
are composed of about 10^5 DM particles. The DM density profiles of the halos
in the 1 Mpc box show systematically shallower cores with respect to the
corresponding halos in the 32 Mpc simulation that have masses, M_{dm}, typical
of the Milky Way and are fitted by a NFW profile. The DM density profiles of
the halos in the 256 Mpc box are consistent with having steeper cores than the
corresponding halos in the 32 Mpc simulation, but higher mass resolution
simulations are needed to strengthen this result. Combined, these results
indicate that the density profile of DM halos is not universal, presenting
shallower cores in dwarf galaxies and steeper cores in clusters. Physically the
result sustains the hypothesis that the mass function of the accreting
satellites determines the inner slope of the DM profile. In comoving
coordinates, r, the profile \rho_{dm} \propto 1/(X^\alpha(1+X)^{3-\alpha}),
with X=c_\Delta r/r_\Delta, r_\Delta is the virial radius and \alpha
=\alpha(M_{dm}), provides a good fit to all the DM halos from dwarf galaxies to
clusters at any redshift with the same concentration parameter c_\Delta ~ 7.
The slope, \gamma, of the outer parts of the halo appears to depend on the
acceleration of the universe: when the scale parameter is a=(1+z)^{-1} < 1, the
slope is \gamma ~ 3 as in the NFW profile, but \gamma ~ 4 at a > 1 when
\Omega_\Lambda ~ 1 and the universe is inflating.[abridged]Comment: Accepted for publication in MNRAS. 13 pages, including 11 figures and
2 tables. The revised version has an additional discussion section and work
on the velocity dispersion anisotrop
Star Formation in a Cosmological Simulation of Reionization
We study the luminosity functions of high-redshift galaxies in detailed
hydrodynamic simulations of cosmic reionization, which are designed to
reproduce the evolution of the Lyman-alpha forest between z=5 and z=6. We find
that the luminosity functions and total stellar mass densities are in agreement
with observations when plausible assumptions about reddenning at z=6 are made.
Our simulations support the conclusion that stars alone reionized the universe.Comment: Accepted for publication in Ap
Knockouts, Robustness and Cell Cycles
The response to a knockout of a node is a characteristic feature of a
networked dynamical system. Knockout resilience in the dynamics of the
remaining nodes is a sign of robustness. Here we study the effect of knockouts
for binary state sequences and their implementations in terms of Boolean
threshold networks. Beside random sequences with biologically plausible
constraints, we analyze the cell cycle sequence of the species Saccharomyces
cerevisiae and the Boolean networks implementing it. Comparing with an
appropriate null model we do not find evidence that the yeast wildtype network
is optimized for high knockout resilience. Our notion of knockout resilience
weakly correlates with the size of the basin of attraction, which has also been
considered a measure of robustness.Comment: 11 pages, 3 figures, 3 table
Quantifying structure in networks
We investigate exponential families of random graph distributions as a
framework for systematic quantification of structure in networks. In this paper
we restrict ourselves to undirected unlabeled graphs. For these graphs, the
counts of subgraphs with no more than k links are a sufficient statistics for
the exponential families of graphs with interactions between at most k links.
In this framework we investigate the dependencies between several observables
commonly used to quantify structure in networks, such as the degree
distribution, cluster and assortativity coefficients.Comment: 17 pages, 3 figure
Neuronal avalanches recorded in the awake and sleeping monkey do not show a power law but can be reproduced by a self-organized critical model
Poster presentation: Self-organized critical (SOC) systems are complex dynamical systems that may express cascades of events, called avalanches [1]. The SOC state was proposed to govern brain function, because of its activity fluctuations over many orders of magnitude, its sensitivity to small input and its long term stability [2,3]. In addition, the critical state is optimal for information storage and processing [4]. Both hallmark features of SOC systems, a power law distribution f(s) for the avalanche size s and a branching parameter (bp) of unity, were found for neuronal avalanches recorded in vitro [5]. However, recordings in vivo yielded contradictory results [6]. Electrophysiological recordings in vivo only cover a small fraction of the brain, while criticality analysis assumes that the complete system is sampled. We hypothesized that spatial subsampling might influence the observed avalanche statistics. In addition, SOC models can have different connectivity, but always show a power law for f(s) and bp = 1 when fully sampled. This may not be the case under subsampling, however. Here, we wanted to know whether a state change from awake to asleep could be modeled by changing the connectivity of a SOC model without leaving the critical state. We simulated a SOC model [1] and calculated f(s) and bp obtained from sampling only the activity of a set of 4 Ă— 4 sites, representing the electrode positions in the cortex. We compared these results with results obtained from multielectrode recordings of local field potentials (LFP) in the cortex of behaving monkeys. We calculated f(s) and bp for the LFP activity recorded while the monkey was either awake or asleep and compared these results to results obtained from two subsampled SOC model with different connectivity. f(s) and bp were very similar for both the experiments and the subsampled SOC model, but in contrast to the fully sampled model, f(s) did not show a power law and bp was smaller than unity. With increasing the distance between the sampling sites, f(s) changed from "apparently supercritical" to "apparently subcritical" distributions in both the model and the LFP data. f(s) and bp calculated from LFP recorded during awake and asleep differed. These changes could be explained by altering the connectivity in the SOC model. Our results show that subsampling can prevent the observation of the characteristic power law and bp in SOC systems, and misclassifications of critical systems as sub- or supercritical are possible. In addition, a change in f(s) and bp for different states (awake/asleep) does not necessarily imply a change from criticality to sub- or supercriticality, but can also be explained by a change in the effective connectivity of the network without leaving the critical state
Correlation in states of two identical particles
We identify the correlation in a state of two identical particles as the
residual information beyond what is already contained in the 1-particle reduced
density matrix, and propose a correlation measure based on the maximum entropy
principle. We obtain the analytical results of the correlation measure, which
make it computable for arbitrary two-particle states. We also show that the
degrees of correlation in the same two-particle states with different particle
types will decrease in the following order: bosons, fermions, and
distinguishable particles.Comment: 3.6 page
Measuring the Nonlinear Biasing Function from a Galaxy Redshift Survey
We present a simple method for evaluating the nonlinear biasing function of
galaxies from a redshift survey. The nonlinear biasing is characterized by the
conditional mean of the galaxy density fluctuation given the underlying mass
density fluctuation, or by the associated parameters of mean biasing and
nonlinearity (following Dekel & Lahav 1999). Using the distribution of galaxies
in cosmological simulations, at smoothing of a few Mpc, we find that the mean
biasing can be recovered to a good accuracy from the cumulative distribution
functions (CDFs) of galaxies and mass, despite the biasing scatter. Then, using
a suite of simulations of different cosmological models, we demonstrate that
the matter CDF is robust compared to the difference between it and the galaxy
CDF, and can be approximated for our purpose by a cumulative log-normal
distribution of 1+\delta with a single parameter \sigma. Finally, we show how
the nonlinear biasing function can be obtained with adequate accuracy directly
from the observed galaxy CDF in redshift space. Thus, the biasing function can
be obtained from counts in cells once the rms mass fluctuation at the
appropriate scale is assumed a priori. The relative biasing function between
different galaxy types is measurable in a similar way. The main source of error
is sparse sampling, which requires that the mean galaxy separation be smaller
than the smoothing scale. Once applied to redshift surveys such as PSCz, 2dF,
SDSS, or DEEP, the biasing function can provide valuable constraints on galaxy
formation and structure evolution.Comment: 23 pages, 7 figures, revised version, accepted for publication in Ap
A new approach to cosmological perturbations in f(R) models
We propose an analytic procedure that allows to determine quantitatively the
deviation in the behavior of cosmological perturbations between a given f(R)
modified gravity model and a LCDM reference model. Our method allows to study
structure formation in these models from the largest scales, of the order of
the Hubble horizon, down to scales deeply inside the Hubble radius, without
employing the so-called "quasi-static" approximation. Although we restrict our
analysis here to linear perturbations, our technique is completely general and
can be extended to any perturbative order.Comment: 21 pages, 2 figures; Revised version according to reviewer's
suggestions; Typos corrected; Added Reference
The Halo Mass Function: High-Redshift Evolution and Universality
We study the formation of dark matter halos in the concordance LCDM model
over a wide range of redshifts, from z=20 to the present. Our primary focus is
the halo mass function, a key probe of cosmology. By performing a large suite
of nested-box N-body simulations with careful convergence and error controls
(60 simulations with box sizes from 4 to 256 Mpc/h, we determine the mass
function and its evolution with excellent statistical and systematic errors,
reaching a few percent over most of the considered redshift and mass range.
Across the studied redshifts, the halo mass is probed over 6 orders of
magnitude (10^7 - 10^13.5 M_sun/h). Historically, there has been considerable
variation in the high redshift mass function as obtained by different groups.
We have made a concerted effort to identify and correct possible systematic
errors in computing the mass function at high redshift and to explain the
discrepancies between some of the previous results. We discuss convergence
criteria for the required force resolution, simulation box size, halo mass
range, initial and final redshift, and time stepping. Because of conservative
cuts on the mass range probed by individual boxes, our results are relatively
insensitive to simulation volume, the remaining sensitivity being consistent
with extended Press-Schechter theory. Previously obtained mass function fits
near z=0, when scaled by linear theory, are in good agreement with our results
at all redshifts, although a mild redshift dependence consistent with that
found by Reed and collaborators exists at low redshifts.Comment: 20 pages, 15 figures. Minor changes to the text and figures; results
and conclusions unchange
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